Nonlinear regression

In statistics, nonlinear regression is a form of regression analysis in which observational data are modeled by a function which is a nonlinear combination of the model parameters and depends on one or more independent variables. The data are fitted by a method of successive approximations.

The data consist of error-free independent variables (explanatory variables), x, and their associated observed dependent variables (response variables), y. Each y is modeled as a random variable with a mean given by a nonlinear function f(x,β). Systematic error may be present but its treatment is outside the scope of regression analysis. If the independent variables are not error-free, this is an errors-in-variables model, also outside this scope.

For example, the Michaelis–Menten model for enzyme kinetics

can be written as

where ${\displaystyle \beta _{1}}$ is the parameter ${\displaystyle V_{\max }}$, ${\displaystyle \beta _{2}}$ is the parameter ${\displaystyle K_{m}}$ and [S] is the independent variable, x. This function is nonlinear because it cannot be expressed as a linear combination of the two ${\displaystyle \beta }$s.

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